If the parent function is y = 4x, which is the function of the graph?

Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coord

ElenaW [278]

Answer:

(0, -1)

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.

Hence for parallelogram RSTU, RS // TU and RU // ST

Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:

Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5

Slope of ST = (2 - 4) /[6 - 3] = -2/3

Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)

Slope of TU = (y - 2) /[x - 6]

Slope of RU = Slope of ST

(y - 1) / (x + 3) = -2/3

3y - 3 = -2x -6

2x + 3y = -6 + 3

2x + 3y = -3 (1)

Slope of RS = Slope of TU

0.5 = (y - 2) /[x - 6]

0.5x - 3 = y - 2

0.5x - y = 1 (2)

Solving 1 and 2 simultaneously gives:

x = 0, y = -1

Therefore the coordinates of U = (0, -1)

8 0

3 years ago

IF U A REAL ONE HELP

lesya [120]

D is the answer hope this helps

4 0

3 years ago

Jennifer is flying from Montana to South Carolina for vacation. Her flight leaves at 6:30 a.m. MST. Her flight is 3 hours. What

snow_lady [41]

11:30 am is the time for south carolina when she lands :)

7 0

2 years ago

PLEASE!!!! I NEED AN ANSWER

MaRussiya [10]

Step-by-step explanation:

I believe this would be A or D

6 0

2 years ago

Sin4x.sin5x+sin4x.sin3x-sin2x.sinx=0

andreev551 [17]

Recall the angle sum identity for cosine:

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

cos(x - y) = cos(x) cos(y) + sin(x) sin(y)

==> sin(x) sin(y) = 1/2 (cos(x - y) - cos(x + y))

Then rewrite the equation as

sin(4x) sin(5x) + sin(4x) sin(3x) - sin(2x) sin(x) = 0

1/2 (cos(-x) - cos(9x)) + 1/2 (cos(x) - cos(7x)) - 1/2 (cos(x) - cos(3x)) = 0

1/2 (cos(9x) - cos(x)) + 1/2 (cos(7x) - cos(3x)) = 0

sin(5x) sin(-4x) + sin(5x) sin(-2x) = 0

-sin(5x) (sin(4x) + sin(2x)) = 0

sin(5x) (sin(4x) + sin(2x)) = 0

Recall the double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

Rewrite the equation again as

sin(5x) (2 sin(2x) cos(2x) + sin(2x)) = 0

sin(5x) sin(2x) (2 cos(2x) + 1) = 0

sin(5x) = 0 or sin(2x) = 0 or 2 cos(2x) + 1 = 0

sin(5x) = 0 or sin(2x) = 0 or cos(2x) = -1/2

sin(5x) = 0 ==> 5x = arcsin(0) + 2nπ or 5x = arcsin(0) + π + 2nπ

… … … … … ==> 5x = 2nπ or 5x = (2n + 1)π

… … … … … ==> x = 2nπ/5 or x = (2n + 1)π/5

sin(2x) = 0 ==> 2x = arcsin(0) + 2nπ or 2x = arcsin(0) + π + 2nπ

… … … … … ==> 2x = 2nπ or 2x = (2n + 1)π

… … … … … ==> x = nπ or x = (2n + 1)π/2

cos(2x) = -1/2 ==> 2x = arccos(-1/2) + 2nπ or 2x = -arccos(-1/2) + 2nπ

… … … … … … ==> 2x = 2π/3 + 2nπ or 2x = -2π/3 + 2nπ

… … … … … … ==> x = π/3 + nπ or x = -π/3 + nπ

(where n is any integer)

5 0

2 years ago